Instability of Wealth Effect on Consumption and Investment Under Regime Switches

Abstract

The instability of wealth effect on consumption over the business cycles is widely recognized in recent empirical studies. We develop a consumption and investment problem for an investor with direct preference for wealth where the drift and volatility of asset return switches between two regimes. Furthermore, the model is extended to allow the investor's borrowing rate to be higher than her risk-free rate. An utility-maximizing policy is derived explicitly such that optimal consumption-wealth ratio depends not only on both current and future regimes, but also on the transition across different regimes. Numerical simulation demonstrates that low frequent changes in regimes produce instability of consumption-wealth ratio, while high frequent regime-shifts produce stable consumption-wealth ratio. These features are enhanced by investor's wealth accumulation motive and tighter credit spread between borrowing rate and risk-free rate, both of which can be applied to explain the instability of consumption-wealth ratio observed in the U.S.